Fractional smoothness of images of logarithmically concave measures under polynomials

Egor D. Kosov

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arXiv · 1605.00162

Fractional smoothness of images of logarithmically concave measures under polynomials

Egor D. Kosov

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Abstract

We show that a measure on the real line that is the image of a log-concave measure under a polynomial of degree $d$ possesses a density from the Nikol'skii--Besov class of fractional order $1/d$. This result is used to prove an estimate of the total variation distance between such measures in terms of the Fortet--Mourier distance.

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Egor D. Kosov. 2016-04-30. Fractional smoothness of images of logarithmically concave measures under polynomials. https://arxiv.org/abs/1605.00162

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